CN104268390A - Method for calculating initial static balanced state of electrified railway contact network - Google Patents

Abstract

The invention discloses an electrified railway contact network static calculation method, comprising the steps of: dispersing the structure of the contact network as units and nodes, using cable units in space to simulate contact lines and carrier cables, using rod units to simulate hanging strings and positioners, assembling a unit tangent matrix of the cable and rod units, assembling an endpoint force column matrix of the cables and the rods, through considering gravities of cable clamps and the hanging strings and taking node coordinates and unit lengths as unknown quantities, constructing a structure incremental balance equation according to unit connecting relation, and thereby completing static calculation of the whole contact network. The electrified railway contact network static calculation method can complete static calculation of the contact network in a three-dimensional space, is applicable to three-dimensional problems of calculating a three-dimensional multi-span contact network or an inclined catenary contact network with a stagger value; the positioner element is added into the calculation, and the calculation method can be applied to different hanging forms such as simple chain hanging and elastic chain hanging and the like, thus being more common in application range.

Description

A kind of electrification railway contact net rest equilibrium state computing method

Technical field

Electrification railway contact net rest equilibrium state computing method of the present invention, for contact net structure in computer memory when there is no External Force Acting, rest equilibrium state on mechanics, as the shape of carrier cable, osculatory in contact net, the distribution of internal force, the gradient of steady arm, the length etc. of dropper, divides according to International Patent Classification (IPC) (IPC) and belongs to operation, Department of Transportation; General vehicle class; The power circuit of electric vehicle or the device group along rail; The technical field of pole line and annex used thereof.

Background technology

Electrifing railway contacting net system is erected at the tension structure to electric locomotive transmission of electric energy on electric railway circuit, is made up of carrier cable, osculatory, dropper, steady arm and wire clamp etc.For obtaining good pantograph-catenary current collection, often a part of contact net structural parameters are determined according to test figure in centenary design, as span, structure height, dropper distribution, pretension, osculatory reserve sag etc., and another part structural parameters are unknown, as the length, stressed of wire, dropper, the curve etc. of wire, and do contact network construction calculate, analyze contact net under external force state change time, need the contact net state knowing that contact net structure is complete when not stressed, namely calculate contact net rest equilibrium state.

At present, large quantity research has been done to the calculating of contact net static balance state both at home and abroad.The people such as Ruan Jie document [foundation [J] of electrified high-speed railway contact net static model. railway society, 2012,34 (8): 20-24] carrier cable, osculatory is analyzed separately with Large travel range beam model, dropper is reduced to acting force coupling carrier cable and osculatory, carry out iterative computation with dropper hitch point equilibrium of forces for control objectives, set up contact net static model, Fang Yan, O Lopez-Garcia respectively document [high speed contact net dropper prewired [J]. Southwest Jiaotong University's journal, 2010, 45 (5): 763-766] and document [Computation of the initial equilibrium of railway overheads based on the catenary equation [J] .Engineering Structures, 2006, (28) adopt based on para-curve hypothesis and accurate cable elements discrete touch net: 1387-1394] respectively, utilize the relation of vertical force and coordinate suffered by bitter end point, build dropper hitch point place equilibrium of forces equation, obtain the coordinate figure of each hitch point.

At present, domestic and international prior art achieves better effects in contact net static calculating, but still has the following disadvantages.First, most research calculates contact net in two dimensional surface, be not suitable for multispan contact net or etc. osculatory, carrier cable not in conplane more generalized case; Secondly, carrier cable, osculatory are separated the thinking of carrying out analyzing and are unfavorable for doing holistic approach to structure; And locator element is not added contact net and together calculates by existing document.

Summary of the invention

The present invention seeks to propose a kind of electrification railway contact net rest equilibrium state computing method.Contact net structural separation is unit and node by the method, adopt cable elements simulating contact line and carrier cable, with bar unit simulation dropper and steady arm, contact net wire clamp is equivalent to quality point, calculates the unit tangent line matrix of rope, bar unit, with node coordinate and element length for unknown quantity, according to unit topological relation, build structural nonlinear balance equation, use alternative manner solving equation, complete the static calculation of overall contact net.The present invention is realized by following concrete technological means:

A, contact net discretize

By discrete at certain intervals to the osculatory of contact net, carrier cable be cable elements, must ensure dropper hitch point place be node, dropper, steady arm are respectively a bar unit.

B, arrange the initial value of unknown quantity in contact net structure, unknown quantity comprises coordinate a little, each unit raw footage before the stretching.

C, assemble each unit tangent line matrix

(1) cable elements tangent line matrix is calculated

Accompanying drawing 1 is 2 cable elements between A, B in three dimensions, F ₁~ F ₆for bitter end power, L ₀for the former length of rope, l _x, l _yand l _zbe respectively A, B 2 spacing in x, y and z direction, E is elastic modulus, and A is sectional area, and w is gravity suffered by unit length, T ₁, T ₂for two ends tension force.

Calculate the tangent stiffness matrix K of each cable elements of contact net about extreme coordinates _c ^ewith the tangent line matrix K about cable elements length _g ^e, such as formula (1).

$K_c^e=\left[\begin{array}{cc}{{-F}_c}^{-1}& {F_c}^{-1}\\ {F_c}^{-1}& {{-F}_c}^{-1}\end{array}\right],K_g^e=\left[\begin{array}{c}-F_c^{-1}{F}_g\\ {\left[\begin{array}{ccc}0& 0& w\end{array}\right]}^T+F_c^{-1}{F}_g\end{array}\right]---\left(1\right)$

In formula (1),

$F_c=\left[\begin{array}{ccc}\frac{\∂l_x}{\∂F_1}& \frac{\∂l_x}{\∂F_2}& \frac{\∂l_x}{\∂F_3}\\ \frac{\∂l_y}{\∂F_1}& \frac{\∂l_y}{\∂F_2}& \frac{\∂l_y}{\∂F_3}\\ \frac{\∂l_z}{\∂F_1}& \frac{\∂l_z}{\∂F_2}& \frac{\∂l_z}{\∂F_3}\end{array}\right],F_g=\left[\begin{array}{c}\frac{\∂l_x}{\∂L_0}\\ \frac{\∂l_y}{\∂L_0}\\ \frac{\∂l_z}{\∂L_0}\end{array}\right]---\left(2\right)$

In formula (2),

$\begin{array}{c}{l}_x=-\frac{F_1{L}_0}{\mathrm{EA}}-\frac{F_1}{w}\{\ln (\sqrt{F_4^2+F_5^2+F_6^2}+F_6)-\ln (\sqrt{F_1^2+F_2^2+F_3^2}-F_3)\}\\ l_y=-\frac{F_2{L}_0}{\mathrm{EA}}-\frac{F_2}{w}\{\ln (\sqrt{F_4^2+F_5^2+F_6^2}+F_6)-\ln (\sqrt{F_1^2+F_2^2+F_3^2}-F_3)\}\\ l_z=-\frac{F_3{L}_0}{\mathrm{EA}}+\frac{w{L}_0^2}{2\mathrm{EA}}+\frac{1}{w}[\sqrt{F_4^2+F_5^2+F_6^2}-\sqrt{F_1^2+F_2^2+F_3^2}]\end{array}---\left(3\right)$

L _x, l _y, l _zexpression formula be the exact formulas of rope section.

(2) bar unit tangent line matrix is calculated

Accompanying drawing 2 is the stressed relation schematic diagram of bar unit.Wherein F ₁~ F ₆for bitter end power, E is elastic modulus, and A is sectional area, L ₀for the former length of bar, L is the length after bar stretches, l _x, l _yand l _zbe respectively A, B 2 spacing in x, y and z direction.Gravity mean allocation suffered by bar unit on two nodes, i.e. F _gA=F _gB=-wL ₀/ 2, w is gravity suffered by unit length.

Calculate the tangent stiffness matrix K of bar unit about node location _c ^ewith the tangent line matrix K about element length _g ^eas follows:

$K_c^e=\left[\begin{array}{cc}-k_c& k_c\\ k_c& -k_c\end{array}\right],K_g^e=\left[\begin{array}{c}{k}_g\\ -k_g\end{array}\right]---\left(4\right)$

In above formula,

$K_c=\left[\begin{array}{ccc}\frac{\∂F_1}{\∂L_x}& \frac{\∂F_1}{\∂L_y}& \frac{\∂F_1}{\∂L_z}\\ \frac{\∂F_2}{\∂L_x}& \frac{\∂F_2}{\∂L_y}& \frac{\∂F_2}{\∂L_z}\\ \frac{\∂F_3}{\∂L_x}& \frac{\∂F_3}{\∂L_y}& \frac{\∂F_3}{\∂L_z}\end{array}\right],K_g=\left[\begin{array}{c}\frac{\∂F_1}{\∂L_0}\\ \frac{\∂F_2}{\∂L_0}\\ \frac{\∂F_3}{\∂L_0}\end{array}\right]---\left(5\right)$

In above formula,

$\begin{array}{c}{F}_1=-\frac{L_x}{L}\·\frac{\mathrm{EA}}{L_0}(L-L_0)\\ F_2=-\frac{L_y}{L}\·\frac{\mathrm{EA}}{L_0}(L-L_0)\\ F_3=-\frac{L_z}{L}\·\frac{\mathrm{EA}}{L_0}(L-L_0)\end{array}---\left(6\right)$

(3) according to the annexation of each unit, module units tangent line matrix, obtains overall tangent line matrix.According to the specified rate in contact net initial equilibrium state, the respective column in cancellation tangent line matrix, such as, in contact net initial equilibrium state, the x of contact line dropper hitch point, z coordinate is known, and therefore in overall tangent line matrix, cancellation arranges accordingly.According to the boundary condition of contact net, utilize penalty function method process tangent line matrix.

D, package assembly out-of-balance force column matrix

(1) each cell terminals power is calculated

1, formula (3) utilization Newton-Raphson process of iteration seeks cell terminals power by reference to the accompanying drawings.Suppose that in formula (3), unknown quantity is F ₁~ F ₃, concrete solution procedure is as follows:

Step 1: input Given information w, EA, L ₀, some A (x _a, y _a, z _a), some B (x _b, y _b, z _b).

Step 2: calculate l _x0=x _a-x _b, l _y0=y _a-y _b, l _z0=z _a-z _b, be F ₁~ F ₃initial value is set.

Step 3: by F ₁~ F ₃l is calculated with formula (1) _x, l _y, l _z, difference

Δl＝{l _x0-l _x l _y0-l _y l _z0-l _z}

Step 4: if || Δ l||>=10 ^-6, enter next step; Otherwise, go to the 6th step.

Step 5: Δ F _a=F _c ^-1Δ l, F _a=F _a+ Δ F _a, go to the 3rd step.

Step 6: finishing iteration, exports F ₁~ F ₃.

F ₁~ F ₃initial value arrange as follows:

$\begin{array}{c}{F}_1=-\frac{{\mathrm{wl}}_x}{2{\mathrm{\λ}}_0}\\ F_2=-\frac{{\mathrm{wl}}_y}{2{\mathrm{\λ}}_0}\\ F_3=\frac{w}{2}(-l_z\frac{\cosh {\mathrm{\λ}}_0}{\sinh {\mathrm{\λ}}_0}+L_0)\end{array}---\left(7\right)$

Wherein

${\mathrm{\λ}}_0=\left\{\begin{array}{cc}{10}^3& ({l_x}^2+{l_y}^2)=0\\ 0.2& {L_0}^2\≤{l_x}^2+{l_y}^2+{l_z}^2\\ \sqrt{3(\frac{L_0-{l_z}^2}{{l_x}^2+{l_y}^2}-1)}& {L_0}^2\≤{l_x}^2+{l_y}^2+{l_z}^2\end{array}\right.---\left(8\right)$

For cable elements prestress problem, as cable elements in accompanying drawing 1, if T ₁known, L ₀the unknown, due to then can solve unknown quantity F ₂, F ₃, L ₀, solution procedure with ask aforementioned and solve F ₁~ F ₃similar.

And for the end points power of bar unit, directly obtain bar unit end points power according to formula.

The gravity of bar unit and wire clamp concentrates in respective nodes.

According to the position assembly node out-of-balance force matrix of unit connection relation and wire clamp.

E, displacement calculating increment

Calculate increment:

ΔX＝K _t ^-1×F (9)

Wherein, Δ X is increment, K _tfor overall tangent line matrix, F is out-of-balance force column matrix.

E, judge whether the maximal value of element absolute value in Δ X is less than 10 ^-6, if so, then calculate, otherwise such as formula renewal contact net structure node coordinate X, and return step C.

X＝X+ΔX (10)

Compared with prior art, the invention has the beneficial effects as follows:

1, the contact net model that the present invention sets up is three-dimensional, can calculate osculatory, the carrier cable situation not in a plane such as multispan contact net and oblique chain contact net.

2, the osculatory of contact net, carrier cable, wire clamp, steady arm calculate by the present invention as a whole, for follow-up holistic approach provides the foundation.

3, calculating of the present invention, steady arm takes into account by contact net structure, makes contact net static model more perfect.

Accompanying drawing explanation

Fig. 1 is a cable elements schematic diagram in space

Fig. 2 is a bar unit schematic diagram in space

Fig. 3 is technical measure process flow diagram

Fig. 4 is contact net structural representation in embodiment one

Fig. 5 is contact net stress and strain model schematic diagram in embodiment one

Fig. 6 is contact net structural representation in embodiment two

Fig. 7 is contact net stress and strain model schematic diagram in embodiment two

Embodiment

Below in conjunction with accompanying drawing, two embodiments of the present invention are elaborated; these two embodiments are applied and simple catenary contact net and elasticity chain contact net respectively; these two embodiments are implemented under premised on technical solution of the present invention; give detailed implementation process, but protection scope of the present invention is not limited to embodiment.

Embodiment one or two hangs contact net across simple catenary

Accompanying drawing 4 is that simple chain contact net two is across schematic diagram.Wherein on the left of osculatory, load bands, right side end points fixes, and right side two line, rope meet tension value T ₁with T ₂, span is l _k, steady arm connects osculatory with certain gradient, and carrier cable can slide in x direction at anchor point place, and steady arm top end points is fixed by hinged, f _cfor the gravity of each hitch point place wire clamp, structure height is h, and the regularity of distribution of dropper in x direction is l _sd-l _dd-...-l _dd-l _sd, one is n across dropper number _d.By accompanying drawing 5 pairs of contact net grid divisions, the carrier cable wherein between dropper, osculatory are divided into a cable elements respectively, and dropper, steady arm are all used as bar unit.In this embodiment, the parameter of contact net is as shown in table 1.

Table 1 embodiment one catenary ' s parameters

The specific implementation process of this embodiment is as follows:

A, make stress and strain model by accompanying drawing 6 pairs of contact nets.

To osculatory, carrier cable, divide a cable elements into by between every two adjacent droppers, each dropper divides a bar unit into, and steady arm divides a bar unit into.

B, the initial coordinate arranging each node of contact net and initial length, this length is the raw footage before pulling.

C, obtain the tangent line matrix of each unit, assemble overall tangent line matrix according to the annexation of each unit, reduce overall tangent line matrix according to the specified rate of contact net initial equilibrium state.Hang simple catenary, specified rate comprises x, y coordinate of contact line dropper hitch point, osculatory steady arm hitch point x, y coordinate, and the x coordinate of steady arm end pin joint, the x coordinate of carrier cable dropper hitch point, carrier cable is at the x, y, z coordinate of anchor point.

D, obtain the end points power of each unit, the gravity of connecting rod unit, wire clamp, assembling one-piece construction out-of-balance force.

E, obtain displacement increment.If increment is less than 10 ^-6, then terminate to calculate, otherwise get back to step C and recalculate.Some numerical results is as shown in table 2 ~ table 4.

Table 2 embodiment one node coordinate

Node	x	y	z	Node	x	y	z	Node	x	y	z
												1	0	0.2	0	12	79	0.032	-0.024	22	45	-0.16	1.4965
2	5	0.16	-0.009	13	87	0.096	-0.019	23	50	-0.2	1.6
												3	13	0.096	-0.019	14	95	0.16	-0.009	24	55	-0.16	1.4965
4	21	0.032	-0.024	15	100	0.2	0	25	63	-0.096	1.3788
												5	29	-0.032	-0.024	16	0	0.2	1.6	26	71	-0.032	1.3202
6	37	-0.096	-0.019	17	5	0.16	1.4965	27	79	0.032	1.3202
												7	45	-0.16	-0.009	18	13	0.096	1.3788	28	87	0.096	1.3788
8	50	-0.2	0	19	21	0.032	1.3202	29	95	0.16	1.4965
												9	55	-0.16	-0.009	20	29	-0.032	1.3202	30	100	0.2	1.6
10	63	-0.096	-0.019	21	37	-0.096	1.3788	31	50	-1.137	0.3483

Table 3 embodiment one unit raw footage

Unit number	1	2	3	4	5	6	7	8	9
										Length (m)	4.9867	7.9787	7.9787	7.9787	7.9787	7.9787	4.9867	4.9867	7.9787
Unit number	10	11	12	13	14	15	16	17	18
										Length (m)	7.9787	7.9787	7.9787	7.9787	4.9867	4.9908	7.9844	7.9837	7.9835
Unit number	19	20	21	22	23	24	25	26	27
										Length (m)	7.9837	7.9844	4.9908	4.9908	7.9844	7.9837	7.9835	7.9837	7.9844
Unit number	28	29	30	31	32	33	34	35	36
										Length (m)	4.9908	1.5046	1.3971	1.3436	1.3436	1.3971	1.5046	1.5046	1.3971
Unit number	37	38	39	40	41
										Length (m)	1.3436	1.3436	1.3971	1.5046	1

In upper table the raw footage of unit and contact network construction calculate in the prewired length of dropper.

Table 4 embodiment one dropper pulling force

Unit number	29	30	31	32	33	34	35	36	37	38	39	40
													Pulling force (N)	56.4	69.5	68.8	68.8	69.5	56.4	56.4	69.5	68.8	68.8	69.5	56.4

Embodiment two liang is across stitched catenary equipment

Accompanying drawing 6 is that stitched catenary equipment contact net two is across schematic diagram.Wherein on the left of osculatory, load bands, right side end points fixes, and right side two line, rope meet tension value T ₁with T ₂, span is l _k, steady arm connects osculatory with certain gradient, and carrier cable can slide in x direction at anchor point place, and steady arm top end points is fixed by hinged, f _cfor the gravity of each hitch point place wire clamp, structure height is h, and the regularity of distribution of dropper in x direction is l _sd-l _dd-...-l _dd-l _sd, one is n across dropper number _d, the span of elastic suspending is l _s, hanger tension is T _s.The be hit by a bullet design parameter of chain contact net of embodiment two is as shown in table 5.

Table 5 example 3 catenary ' s parameters

The specific implementation process of this embodiment is as follows:

A, make stress and strain model by accompanying drawing 7 pairs of contact nets.

To osculatory, carrier cable, divide a cable elements into by between every two adjacent droppers, each dropper divides a bar unit into, and steady arm divides a bar unit into.

B, the initial coordinate arranging each node of contact net and initial length, this length is the raw footage before pulling.

C, obtain the tangent line matrix of each unit, assemble overall tangent line matrix according to the annexation of each unit, reduce overall tangent line matrix according to the specified rate of contact net initial equilibrium state.To stitched catenary equipment, specified rate comprises x, y coordinate of contact line dropper hitch point, osculatory steady arm hitch point x, y, z coordinate, the x coordinate of steady arm end pin joint, the x coordinate of carrier cable dropper hitch point, elastic suspending hitch point x coordinate, carrier cable at the x, y, z coordinate of anchor point, osculatory, carrier cable, elastic suspending tension force.

D, obtain the end points power of each unit, the gravity of connecting rod unit, wire clamp, assembling one-piece construction out-of-balance force.

E, obtain displacement increment.If increment is less than 10 ^-6, then terminate to calculate, otherwise get back to step C and recalculate.

Embodiment two some numerical results is as shown in table 6 ~ table 8.

Table 6 embodiment two node coordinate

Node	x	y	z	Node	x	y	z	Node	x	y	z
												1	0	0.3	0	14	106.67	0.0855	0	27	70	-0.2077	1.3613
2	5	0.254047	0	15	115.83	0.1698	0	28	74	-0.2047	1.4755
												3	14.167	0.16979	0	16	125	0.254	0	29	65	-0.3	1.8
4	23.333	0.085483	0	17	130	0.3	0	30	79.167	-0.1585	1.3666
												5	32.5	0.001082	0	18	0	0.3	1.8	31	88.333	-0.0762	1.25

6	41.667	-0.08346	0	19	5	0.2548	1.6403	32	97.5	0.0063	1.2191
												7	50.833	-0.1682	0	20	14.167	0.1719	1.4142	33	106.67	0.08903	1.2738
8	60	-0.25317	0	21	23.333	0.089	1.2738	34	115.83	0.17187	1.4142
												9	65	-0.3	0	22	32.5	0.0063	1.2191	35	125	0.25477	1.6403
10	70	-0.25317	0	23	41.667	-0.076	1.25	36	130	0.3	1.8
												11	79.167	-0.1682	0	24	50.833	-0.159	1.3666	37	65	-1.2922	0.1243
12	88.333	-0.08346	0	25	56	-0.205	1.4755
												13	97.5	0.001082	0	26	60	-0.208	1.3613

Table 7 embodiment two unit raw footage

Unit	1	2	3	4	5	6	7	8	9	10
											Former length	4.9909	9.1499	9.1499	9.1499	9.1499	9.1499	9.1499	4.9909	4.9909	9.1499
Unit	11	12	13	14	15	16	17	18	19	20
											Former length	9.1499	9.1499	9.1499	9.1499	9.1499	4.9909	1.6402	1.4141	1.2737	1.219
Unit	21	22	23	24	25	26	27	28	29	30
											Former length	1.2499	1.3665	1.362	1.362	1.3665	1.2499	1.219	1.2737	1.4141	1.6402
Unit	31	32	33	34	35	36	37	38	39	40
											Former length	4.9955	9.1565	9.1548	9.1539	9.1538	9.1544	5.1605	3.9984	9.9919	3.9984
Unit	41	42	43	44	45	46	47	48	49	50
											Former length	8.9954	8.9954	5.1605	9.1544	9.1538	9.1539	9.1548	9.1565	4.9955	1

The pulling force of table 8 embodiment two dropper:

Unit number	17	18	19	20	21	22	23	24	25	26	27	28	29	30
															Pulling force	76.9	98.8	98.8	98.7	98.8	98.8	76.8	76.8	98.8	98.8	98.7	98.8	98.8	76.8

Claims (4)

1. electrification railway contact net rest equilibrium state computing method, for contact net structure rest equilibrium state in computer memory, by being unit and node by contact net structural separation, cable elements simulating contact line and carrier cable, with bar unit simulation dropper and steady arm, assembled cable, the unit tangent line matrix of bar unit, assembled cable, the end points power column matrix of bar, consider wire clamp, the gravity of dropper, with node coordinate and element length for unknown quantity, according to unit connection relation, build the static calculation that structure increment balance equation completes overall contact net, comprise following concrete steps:

A, contact net discretize

By discrete at certain intervals to the osculatory of contact net, carrier cable be cable elements, must ensure dropper hitch point place be node, dropper, steady arm are respectively a bar unit;

B, arrange the initial value of unknown quantity in contact net structure, unknown quantity comprises coordinate a little, each unit raw footage before the stretching;

C, assemble each unit tangent line matrix;

(1) cable elements tangent line matrix is calculated

2 cable elements between A, B in three dimensions, F ₁~ F ₆for bitter end power, L ₀for the former length of rope, l _x, l _yand l _zbe respectively A, B 2 spacing in x, y and z direction, E is elastic modulus, and A is sectional area, and w is gravity suffered by unit length, T ₁, T ₂for two ends tension force;

Calculate the tangent stiffness matrix K of each cable elements of contact net about extreme coordinates _c ^ewith the tangent line matrix K about cable elements length _g ^e, such as formula (1);

$K_c^e=\left[\begin{array}{cc}{{-F}_c}^{-1}& {F_c}^{-1}\\ {F_c}^{-1}& {{-F}_c}^{-1}\end{array}\right],K_g^e=\left[\begin{array}{c}-F_c^{-1}{F}_g\\ {\left[\begin{array}{ccc}0& 0& w\end{array}\right]}^T+F_c^{-1}{F}_g\end{array}\right]---\left(1\right)$

In formula (1),

$F_c=\left[\begin{array}{ccc}\frac{\∂l_x}{\∂F_1}& \frac{\∂l_x}{\∂F_2}& \frac{\∂l_x}{\∂F_3}\\ \frac{\∂l_y}{\∂F_1}& \frac{\∂l_y}{\∂F_2}& \frac{\∂l_y}{\∂F_3}\\ \frac{\∂l_z}{\∂F_1}& \frac{\∂l_z}{\∂F_2}& \frac{\∂l_z}{\∂F_3}\end{array}\right],F_g=\left[\begin{array}{c}\frac{\∂l_x}{\∂L_0}\\ \frac{\∂l_y}{\∂L_0}\\ \frac{\∂l_z}{\∂L_0}\end{array}\right]---\left(2\right)$

In formula (2),

$\begin{array}{c}{l}_x=-\frac{F_1{L}_0}{\mathrm{EA}}-\frac{F_1}{w}\{\ln (\sqrt{F_4^2+F_5^2+F_6^2}+F_6)-\ln (\sqrt{F_1^2+F_2^2+F_3^2}-F_3)\}\\ l_y=-\frac{F_2{L}_0}{\mathrm{EA}}-\frac{F_2}{w}\{\ln (\sqrt{F_4^2+F_5^2+F_6^2}+F_6)-\ln (\sqrt{F_1^2+F_2^2+F_3^2}-F_3)\}\\ l_z=-\frac{F_3{L}_0}{\mathrm{EA}}+\frac{w{L}_0^2}{2\mathrm{EA}}+\frac{1}{w}[\sqrt{F_4^2+F_5^2+F_6^2}-\sqrt{F_1^2+F_2^2+F_3^2}]\end{array}---\left(3\right)$

L _x, l _y, l _zexpression formula be the exact formulas of rope section;

(2) bar unit tangent line matrix is calculated

Calculate the tangent stiffness matrix K of bar unit about node location _c ^ewith the tangent line matrix K about element length _g ^eas follows:

$K_c^e=\left[\begin{array}{cc}-k_c& k_c\\ k_c& -k_c\end{array}\right],K_g^e=\left[\begin{array}{c}{k}_g\\ -k_g\end{array}\right]---\left(4\right)$

In above formula,

$K_c=\left[\begin{array}{ccc}\frac{\∂F_1}{\∂L_x}& \frac{\∂F_1}{\∂L_y}& \frac{\∂F_1}{\∂L_z}\\ \frac{\∂F_2}{\∂L_x}& \frac{\∂F_2}{\∂L_y}& \frac{\∂F_2}{\∂L_z}\\ \frac{\∂F_3}{\∂L_x}& \frac{\∂F_3}{\∂L_y}& \frac{\∂F_3}{\∂L_z}\end{array}\right],K_g=\left[\begin{array}{c}\frac{\∂F_1}{\∂L_0}\\ \frac{\∂F_2}{\∂L_0}\\ \frac{\∂F_3}{\∂L_0}\end{array}\right]---\left(5\right)$

In above formula,

$\begin{array}{c}{F}_1=-\frac{L_x}{L}\·\frac{\mathrm{EA}}{L_0}(L-L_0)\\ F_2=-\frac{L_y}{L}\·\frac{\mathrm{EA}}{L_0}(L-L_0)\\ F_3=-\frac{L_z}{L}\·\frac{\mathrm{EA}}{L_0}(L-L_0)\end{array}---\left(6\right)$

Wherein F ₁~ F ₆for bitter end power, E is elastic modulus, and A is sectional area, L ₀for the former length of bar, L is the length after bar stretches, l _x, l _yand l _zbe respectively A, B 2 spacing in x, y and z direction; Gravity mean allocation suffered by bar unit on two nodes, i.e. F _gA=F _gB=-wL ₀/ 2, w is gravity suffered by unit length;

(3) according to the annexation of each unit, module units tangent line matrix, obtains overall tangent line matrix; According to the boundary condition of contact net, utilize penalty function method process tangent line matrix;

D, package assembly out-of-balance force column matrix

(1) each cell terminals power is calculated

Newton-Raphson process of iteration is used to seek cell terminals power; Suppose that in formula (3), unknown quantity is F ₁~ F ₃, concrete solution procedure is as follows:

Step 1: input Given information w, EA, L ₀, some A (x _a, y _a, z _a), some B (x _b, y _b, z _b);

Step 2: calculate l _x0=x _a-x _b, l _y0=y _a-y _b, l _z0=z _a-z _b, be F ₁~ F ₃initial value is set;

Step 3: by F ₁~ F ₃l is calculated with formula (1) _x, l _y, l _z, difference

Δl＝{l _x0-l _x l _y0-l _y l _z0-l _z}

Step 4: if || Δ l||>=10 ^-6, enter next step; Otherwise, go to the 6th step;

Step 5: Δ F _a=F _c ^-1Δ l, F _a=F _a+ Δ F _a, go to the 3rd step;

Step 6: finishing iteration, exports F ₁~ F ₃;

F ₁~ F ₃initial value arrange as follows:

$\begin{array}{c}{F}_1=-\frac{{\mathrm{wl}}_x}{2{\mathrm{\λ}}_0}\\ F_2=-\frac{{\mathrm{wl}}_y}{2{\mathrm{\λ}}_0}\\ F_3=\frac{w}{2}(-l_z\frac{\cosh {\mathrm{\λ}}_0}{\sinh {\mathrm{\λ}}_0}+L_0)\end{array}---\left(7\right)$

Wherein

${\mathrm{\λ}}_0=\left\{\begin{array}{cc}{10}^3& ({l_x}^2+{l_y}^2)=0\\ 0.2& {L_0}^2\≤{l_x}^2+{l_y}^2+{l_z}^2\\ \sqrt{3(\frac{L_0-{l_z}^2}{{l_x}^2+{l_y}^2}-1)}& {L_0}^2\≤{l_x}^2+{l_y}^2+{l_z}^2\end{array}\right.---\left(8\right)$

For cable elements prestress problem, as cable elements in accompanying drawing 1, if T ₁known, L ₀the unknown, due to then can solve unknown quantity F ₂, F ₃, L ₀, solution procedure with ask aforementioned and solve F ₁~ F ₃similar;

And for the end points power of bar unit, directly obtain bar unit end points power according to formula;

The gravity of bar unit and wire clamp concentrates in respective nodes, according to the position assembly node out-of-balance force matrix of unit connection relation and wire clamp;

E, displacement calculating increment

Calculate increment:

ΔX＝K _t ^-1×F (9)

Wherein, Δ X is increment, K _tfor overall tangent line matrix, F is out-of-balance force column matrix;

E, judge whether the maximal value of element absolute value in Δ X is less than 10 ^-6, if so, then calculate, otherwise such as formula renewal contact net structure node coordinate X, and return step C;

X＝X+ΔX。

2. electrification railway contact net rest equilibrium state computing method according to claim 1, it is characterized in that: the tangent line matrix of described rope, bar unit, comprising: coordinate unit end points power to the tangent stiffness matrix of cell node coordinate and cell terminals power to the tangent line matrix of unit raw footage.

3. electrification railway contact net rest equilibrium state computing method according to claim 1, is characterized in that: described cable elements end points power Newton-Raphson process of iteration calculates.

4. electrification railway contact net rest equilibrium state computing method according to claim 1, is characterized in that: described wire clamp gravity is concentrated and acted on node, and dropper gravity peptizaiton is on two end nodes of dropper.